The discussion centers on the output of the Mathematica plotting function for the expression involving Jacobi elliptic functions. Specifically, the user queries why the output of the expression k^2 JacobiSN[t, k]^2 + JacobiDN[t, k]^2 does not yield a constant value of 1 as expected. Participants confirm that the output oscillates between 1 and 2 in Mathematica version 12.0.0.0, and clarify that the correct interpretation involves understanding the parameters of JacobiSN and JacobiDN, particularly that the second argument should be the modulus m, not k.
Mathematics students, researchers using Mathematica, and anyone working with elliptic functions and their graphical representations.
k = 2;
Plot[k^2 JacobiSN[t, k]^2 + JacobiDN[t, k]^2, {t, 0, 10}]Yes, that oscillates between 1 and 2 (Mathematica 12.0.0.0).joshmccraney said:Can anyone confirm if the following in Mathematica gives an output that is not 1? I'm getting some sort of sinusoid, but I should get 1.
Code:k = 2; Plot[k^2 JacobiSN[t, k]^2 + JacobiDN[t, k]^2, {t, 0, 10}]
Thanks!
But the addition theorems here https://en.wikipedia.org/wiki/Jacobi_elliptic_functions imply ##k^2 sn^2 + dn^2 = 1##? Am I missing something?DrClaude said:Yes, that oscillates between 1 and 2 (Mathematica 12.0.0.0).
Plot[2 JacobiSN[t, k]^2 + JacobiDN[t, k]^2, {t, 0, 10}]Do you mean ##k^2## instead of 4?Bill Simpson said:I don't know if this helps, but
Code:Plot[2 JacobiSN[t, k]^2 + JacobiDN[t, k]^2, {t, 0, 10}]
does appear to be 1 for all values of t while 4 JacobiSN[t, k]^2 + JacobiDN[t, k]^2 is not.
I noticed that by plotting the two functions separately and guessing the needed scale factor.